// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2017 Kyle Macfarlan <kyle.macfarlan@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_KLUSUPPORT_H
#define EIGEN_KLUSUPPORT_H

namespace Eigen {

/* TODO extract L, extract U, compute det, etc... */

/** \ingroup KLUSupport_Module
  * \brief A sparse LU factorization and solver based on KLU
  *
  * This class allows to solve for A.X = B sparse linear problems via a LU factorization
  * using the KLU library. The sparse matrix A must be squared and full rank.
  * The vectors or matrices X and B can be either dense or sparse.
  *
  * \warning The input matrix A should be in a \b compressed and \b column-major form.
  * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
  * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
  *
  * \implsparsesolverconcept
  *
  * \sa \ref TutorialSparseSolverConcept, class UmfPackLU, class SparseLU
  */

inline int klu_solve(klu_symbolic* Symbolic, klu_numeric* Numeric, Index ldim, Index nrhs, double B[], klu_common* Common, double)
{
    return klu_solve(Symbolic, Numeric, internal::convert_index<int>(ldim), internal::convert_index<int>(nrhs), B, Common);
}

inline int klu_solve(klu_symbolic* Symbolic, klu_numeric* Numeric, Index ldim, Index nrhs, std::complex<double> B[], klu_common* Common, std::complex<double>)
{
    return klu_z_solve(Symbolic, Numeric, internal::convert_index<int>(ldim), internal::convert_index<int>(nrhs), &numext::real_ref(B[0]), Common);
}

inline int klu_tsolve(klu_symbolic* Symbolic, klu_numeric* Numeric, Index ldim, Index nrhs, double B[], klu_common* Common, double)
{
    return klu_tsolve(Symbolic, Numeric, internal::convert_index<int>(ldim), internal::convert_index<int>(nrhs), B, Common);
}

inline int klu_tsolve(klu_symbolic* Symbolic, klu_numeric* Numeric, Index ldim, Index nrhs, std::complex<double> B[], klu_common* Common, std::complex<double>)
{
    return klu_z_tsolve(Symbolic, Numeric, internal::convert_index<int>(ldim), internal::convert_index<int>(nrhs), &numext::real_ref(B[0]), 0, Common);
}

inline klu_numeric* klu_factor(int Ap[], int Ai[], double Ax[], klu_symbolic* Symbolic, klu_common* Common, double)
{
    return klu_factor(Ap, Ai, Ax, Symbolic, Common);
}

inline klu_numeric* klu_factor(int Ap[], int Ai[], std::complex<double> Ax[], klu_symbolic* Symbolic, klu_common* Common, std::complex<double>)
{
    return klu_z_factor(Ap, Ai, &numext::real_ref(Ax[0]), Symbolic, Common);
}

template <typename _MatrixType> class KLU : public SparseSolverBase<KLU<_MatrixType>>
{
protected:
    typedef SparseSolverBase<KLU<_MatrixType>> Base;
    using Base::m_isInitialized;

public:
    using Base::_solve_impl;
    typedef _MatrixType MatrixType;
    typedef typename MatrixType::Scalar Scalar;
    typedef typename MatrixType::RealScalar RealScalar;
    typedef typename MatrixType::StorageIndex StorageIndex;
    typedef Matrix<Scalar, Dynamic, 1> Vector;
    typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
    typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
    typedef SparseMatrix<Scalar> LUMatrixType;
    typedef SparseMatrix<Scalar, ColMajor, int> KLUMatrixType;
    typedef Ref<const KLUMatrixType, StandardCompressedFormat> KLUMatrixRef;
    enum
    {
        ColsAtCompileTime = MatrixType::ColsAtCompileTime,
        MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
    };

public:
    KLU() : m_dummy(0, 0), mp_matrix(m_dummy) { init(); }

    template <typename InputMatrixType> explicit KLU(const InputMatrixType& matrix) : mp_matrix(matrix)
    {
        init();
        compute(matrix);
    }

    ~KLU()
    {
        if (m_symbolic)
            klu_free_symbolic(&m_symbolic, &m_common);
        if (m_numeric)
            klu_free_numeric(&m_numeric, &m_common);
    }

    EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return mp_matrix.rows(); }
    EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return mp_matrix.cols(); }

    /** \brief Reports whether previous computation was successful.
      *
      * \returns \c Success if computation was successful,
      *          \c NumericalIssue if the matrix.appears to be negative.
      */
    ComputationInfo info() const
    {
        eigen_assert(m_isInitialized && "Decomposition is not initialized.");
        return m_info;
    }
#if 0  // not implemented yet
    inline const LUMatrixType& matrixL() const
    {
      if (m_extractedDataAreDirty) extractData();
      return m_l;
    }

    inline const LUMatrixType& matrixU() const
    {
      if (m_extractedDataAreDirty) extractData();
      return m_u;
    }

    inline const IntColVectorType& permutationP() const
    {
      if (m_extractedDataAreDirty) extractData();
      return m_p;
    }

    inline const IntRowVectorType& permutationQ() const
    {
      if (m_extractedDataAreDirty) extractData();
      return m_q;
    }
#endif
    /** Computes the sparse Cholesky decomposition of \a matrix
     *  Note that the matrix should be column-major, and in compressed format for best performance.
     *  \sa SparseMatrix::makeCompressed().
     */
    template <typename InputMatrixType> void compute(const InputMatrixType& matrix)
    {
        if (m_symbolic)
            klu_free_symbolic(&m_symbolic, &m_common);
        if (m_numeric)
            klu_free_numeric(&m_numeric, &m_common);
        grab(matrix.derived());
        analyzePattern_impl();
        factorize_impl();
    }

    /** Performs a symbolic decomposition on the sparcity of \a matrix.
      *
      * This function is particularly useful when solving for several problems having the same structure.
      *
      * \sa factorize(), compute()
      */
    template <typename InputMatrixType> void analyzePattern(const InputMatrixType& matrix)
    {
        if (m_symbolic)
            klu_free_symbolic(&m_symbolic, &m_common);
        if (m_numeric)
            klu_free_numeric(&m_numeric, &m_common);

        grab(matrix.derived());

        analyzePattern_impl();
    }

    /** Provides access to the control settings array used by KLU.
      *
      * See KLU documentation for details.
      */
    inline const klu_common& kluCommon() const { return m_common; }

    /** Provides access to the control settings array used by UmfPack.
      *
      * If this array contains NaN's, the default values are used.
      *
      * See KLU documentation for details.
      */
    inline klu_common& kluCommon() { return m_common; }

    /** Performs a numeric decomposition of \a matrix
      *
      * The given matrix must has the same sparcity than the matrix on which the pattern anylysis has been performed.
      *
      * \sa analyzePattern(), compute()
      */
    template <typename InputMatrixType> void factorize(const InputMatrixType& matrix)
    {
        eigen_assert(m_analysisIsOk && "KLU: you must first call analyzePattern()");
        if (m_numeric)
            klu_free_numeric(&m_numeric, &m_common);

        grab(matrix.derived());

        factorize_impl();
    }

    /** \internal */
    template <typename BDerived, typename XDerived> bool _solve_impl(const MatrixBase<BDerived>& b, MatrixBase<XDerived>& x) const;

#if 0  // not implemented yet
    Scalar determinant() const;

    void extractData() const;
#endif

protected:
    void init()
    {
        m_info = InvalidInput;
        m_isInitialized = false;
        m_numeric = 0;
        m_symbolic = 0;
        m_extractedDataAreDirty = true;

        klu_defaults(&m_common);
    }

    void analyzePattern_impl()
    {
        m_info = InvalidInput;
        m_analysisIsOk = false;
        m_factorizationIsOk = false;
        m_symbolic = klu_analyze(internal::convert_index<int>(mp_matrix.rows()),
                                 const_cast<StorageIndex*>(mp_matrix.outerIndexPtr()),
                                 const_cast<StorageIndex*>(mp_matrix.innerIndexPtr()),
                                 &m_common);
        if (m_symbolic)
        {
            m_isInitialized = true;
            m_info = Success;
            m_analysisIsOk = true;
            m_extractedDataAreDirty = true;
        }
    }

    void factorize_impl()
    {
        m_numeric = klu_factor(const_cast<StorageIndex*>(mp_matrix.outerIndexPtr()),
                               const_cast<StorageIndex*>(mp_matrix.innerIndexPtr()),
                               const_cast<Scalar*>(mp_matrix.valuePtr()),
                               m_symbolic,
                               &m_common,
                               Scalar());

        m_info = m_numeric ? Success : NumericalIssue;
        m_factorizationIsOk = m_numeric ? 1 : 0;
        m_extractedDataAreDirty = true;
    }

    template <typename MatrixDerived> void grab(const EigenBase<MatrixDerived>& A)
    {
        mp_matrix.~KLUMatrixRef();
        ::new (&mp_matrix) KLUMatrixRef(A.derived());
    }

    void grab(const KLUMatrixRef& A)
    {
        if (&(A.derived()) != &mp_matrix)
        {
            mp_matrix.~KLUMatrixRef();
            ::new (&mp_matrix) KLUMatrixRef(A);
        }
    }

    // cached data to reduce reallocation, etc.
#if 0  // not implemented yet
    mutable LUMatrixType m_l;
    mutable LUMatrixType m_u;
    mutable IntColVectorType m_p;
    mutable IntRowVectorType m_q;
#endif

    KLUMatrixType m_dummy;
    KLUMatrixRef mp_matrix;

    klu_numeric* m_numeric;
    klu_symbolic* m_symbolic;
    klu_common m_common;
    mutable ComputationInfo m_info;
    int m_factorizationIsOk;
    int m_analysisIsOk;
    mutable bool m_extractedDataAreDirty;

private:
    KLU(const KLU&) {}
};

#if 0  // not implemented yet
template<typename MatrixType>
void KLU<MatrixType>::extractData() const
{
  if (m_extractedDataAreDirty)
  {
     eigen_assert(false && "KLU: extractData Not Yet Implemented");

    // get size of the data
    int lnz, unz, rows, cols, nz_udiag;
    umfpack_get_lunz(&lnz, &unz, &rows, &cols, &nz_udiag, m_numeric, Scalar());

    // allocate data
    m_l.resize(rows,(std::min)(rows,cols));
    m_l.resizeNonZeros(lnz);

    m_u.resize((std::min)(rows,cols),cols);
    m_u.resizeNonZeros(unz);

    m_p.resize(rows);
    m_q.resize(cols);

    // extract
    umfpack_get_numeric(m_l.outerIndexPtr(), m_l.innerIndexPtr(), m_l.valuePtr(),
                        m_u.outerIndexPtr(), m_u.innerIndexPtr(), m_u.valuePtr(),
                        m_p.data(), m_q.data(), 0, 0, 0, m_numeric);

    m_extractedDataAreDirty = false;
  }
}

template<typename MatrixType>
typename KLU<MatrixType>::Scalar KLU<MatrixType>::determinant() const
{
  eigen_assert(false && "KLU: extractData Not Yet Implemented");
  return Scalar();
}
#endif

template <typename MatrixType>
template <typename BDerived, typename XDerived>
bool KLU<MatrixType>::_solve_impl(const MatrixBase<BDerived>& b, MatrixBase<XDerived>& x) const
{
    Index rhsCols = b.cols();
    EIGEN_STATIC_ASSERT((XDerived::Flags & RowMajorBit) == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
    eigen_assert(m_factorizationIsOk &&
                 "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");

    x = b;
    int info = klu_solve(m_symbolic, m_numeric, b.rows(), rhsCols, x.const_cast_derived().data(), const_cast<klu_common*>(&m_common), Scalar());

    m_info = info != 0 ? Success : NumericalIssue;
    return true;
}

}  // end namespace Eigen

#endif  // EIGEN_KLUSUPPORT_H
